How to make phosphorescent material
I provided a video for better clarification, also used Eevee because the render is fast, but you can use cycles too.

What you want is to simply animate a emission property and a light brightness, in the case of cycles, you could use only the emission shader.

You will also need another shader when the light fades off, so you mix the emission with the other shader, for a nice effect, I applied the same texture to the emitter. To the sphere to not cast shadow, I simply set the shadows to none in the materials tab.